Articles A64. NR filled with silica or carbon black. [10]

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1 Almost any rubber that is used for reallife applications is a highly complex, heterogeneous material consisting of a cross linked polymer matrix (an elastomer) and significant amounts of inorganic, often nanometersized particles such as carbon black or silica. [13] Without such fillers, rubber materials would not exhibit the favourable and fascinating combination of properties such as elasticity, large deformability, high toughness, durability (abrasion resistance) and, in particular when tire applications are in the focus, traction on wet or icy roads and low viscous losses (low rolling resistence). In particular the optimization of the latter while not compromising the other relevant properties, related to the development of green tires for lower fuel consumption, is a field of active industrial development that is characterized by a lack of rational design principles and an indepth theoretical understanding. Some aspects of the complex mechanical behaviour of filled elastomers are highlighted in Fig. 1, where in the sketch in Fig. 1a it is emphasized that the spatial distribution of the nanoparticles plays a key role. In most applicationrelevant cases, the particles themselves form a network with a complex structural hierarchy over many decades in length scale, [1,3] starting at primary particles on the fewnm range, via aggregates and agglomerates, finally forming a macroscopically percolated structure that can transmit mechanical load. To illustrate its effect, Fig. 1b shows the storage modulus (100 Hz) from frequency dependent shear experiments of the industrially relevant tire material SBR (styrenebutadiene rubber) as a function of tempe rature. [4] The large drop in over 3 decades marks the glass transition of the matrix at around 15C. While in the ensuing rubber plateau region, unfilled SBR exhibits the expected positive temperature dependence as expected from the entropic models of rubber elasticity, filled SBR has a much higher modulus which usually significantly on heating. This is emphasized by [5] plotting the reinforcement factor () = filled / unfilled at constant temperature difference to the glass transition shown in the inset, which is seen to be highest at temperatures around and above the glassrubber transition. While below, the low reinforcement can be explained on the basis of simply considering the additive effect of a certain volume of high moduls material, values exceeding = 10 indicate the important synergistic effect of a filler network. Importantly, the decrease of at even higher temperatures indicates nontrivial interfacial effects of the polymerfiller system that are in the focus of our research initiative. Based on such observations, some of us [5] have previously developed a model based on the existence of a glassy layer of immobilized polymer material on the particle surface that constitutes a sticker between the particles and simply softens at higher temperature. [6,7] Other important features of filled rubbers that must ultimately be captured by a quantitative model are the wellknown dramatic decrease of in the range of higher deformations, the socalled Payne effect that can be attributed to a mechanical breakdown of the filler network, and history and hysteresis effects under conditions of cyclic mechanical load, so called Mullins effects, related to the evolution of structural com plexity. [2,3] Preliminary NMR experiments on a welldispersed model system have indeed provided direct evidence of an interphase consisting of immobilized polymer. [8] These studies provided the starting point for the present work, where we seek to systematically study such interphase fractions and their impact on the macroscopic properties. Notably, in systems that are closer to actual applications, having much more inhomogeneous particle dispersions, interphases have as yet not been observed directly. Rather, the existence of glassy layers was for the case of carbon black indirectly inferred from socalled boundrubber extraction or dielectric experiments, [13,9] or from fits of mechanical models to rheological data. [3] Direct studies by advanced NMR methods have as yet neither revealed significant amounts of A63

2 Articles once means that structural inhomogeneity, i.e., the coexistence of lowly and highly crosslinked regions, is directly reflected in the data. For the given method, it is possible to extract the of the RDC, which directly reflects the distribution in local crosslink densities. The data in Fig. 1c is typical in that, first, vulcanized elastomers were commonly found to be very homogeneous, and second, that fillers of any type hardly affect this homogeneity. The only significant filler effect turned out to be the observation that the crosslink density in a filled system is always somewhat lower that that of the unfilled counterpart, which is straightforwardly attributed to a partial deactivation of the vulcanization system by the highsurface filler. The conclusion is clear: if effects of glassy layers or locally modified crosslink density should be responsible for the mechanical properties (Fig. 1b), their volume fraction must be very low, i.e. below the limit of NMR detectability on the percent level. If can of course be imagined that in aggregated/agglomera ted systems, the internal surface is much lower as compared to isolated nanofillers, such that even small amounts of interphase material close to the particles can affect large changes of the total system. The important question to be resolved in our work is now to establish a link between tunable model systems, which as shown below do exhibit the mentioned features of glassy layers and inhomogeneous rubber matrix, and the systems of application relevance. (a) Inhomogeneous nanoparticle distribution in a filled rubber for, e.g., tire applications. Tire image by courtesy of Continental AG. (b) Storage moduls at a shear frequency of 100 Hz of unfilled vs. silicafilled SBR as a function of tempe rature. The inset shows the reinforcement = filled/ unfilled as a function of temperature difference to the glass transition. Data from ref. [4]. (c) Distributions of crosslink density, as measured in terms of the RDC taken from NMR experiments, for pure NR and NR filled with silica or carbon black. [10] glassy layer, nor did they give any indication of substantial changes in the network matrix. Corresponding results from the Halle lab in collaboration with the ICTPCSIC in Madrid are shown in Fig. 1c. In a broad study comprising a wide range of traditional and modern nanofillers in commercially relevant rubber materials, NR (natural rubber) and SBR, revealed substantial effect of any filler on the actual rubber matrix. [10] One of the NMR methods used, namely 1 H multiplequantum (MQ) NMR, [11] is able to provide information on the crosslink density ν c of the materials based on network chain mobility. Its result is the so called residual dipolar coupling (RDC) constant associated with the protons in each monomer. Generally, the RDC is directly proportional to the crosslink density, or to the number of elastically active network chains of weight c in the sample, which in turn determines the modulus. Thus, RDC ν c 1/ c. The feature that 1 H NMR detects all monomers at Industrial samples are simply made by strong mechanical mixing of all the constituents: solid particles, grafting agent and surfactant, polymer, crosslinker, and various catalysts. The spatial arrangement of the nanoparticles is far from equilibrium and depends crucially on the energy and time of mixing. Indeed, during the mixing, it is known that the molecular weights of the chains decrease, probably in a different manner for the polymer adsorbed at the particle surface and in the bulk. Thus the mechanical properties are relatively sensitive to mixing conditions. In addition, it is also known that the time elapsed between mixing and crosslinking (curing by, e.g. vulcanisation) has an influence on the mechanical properties because of slow rearrangements of the nanoparticles. Lastly, the surface agents grafters and surfactants are also known to modify the arrange ment of the nanoparticles in the samples. This complexity has unfortunately hindered the understanding of the physics of these systems. Thus, it is crucial in order to get quantitative and comprehensive experimental results both to synthesize model nanocomposites with extremely wellcontrolled arrangement and to be able to characterize their nanoparticles arrangements. The characterization is rather simple if we are able to use spherical nearly polydisperse nanoparticles. The most versatile particles for that are silica particles that are easy to prepare, and to modify A64

3 chemically. Moreover, they exhibit a natural contrast against the polymer for neutron scattering experiments. [12] The trick we have been using in recent years was to prepare solutions of colloidal silica particles in a solvent consisting of the monomers with crosslinker and eventually additional solvent and to polymerize and crosslink the monomer controlling the colloidal stability during the whole process. This was quite simple in the case of polyacrylates specifically poly(ethyl acrylate), PEA and has allowed us to get systems with nearly crystalline arrangement of nanoparticles. [12] Thanks to these samples, we were thus the first to put into evidence the effect of gradient of glass transition temperature in nanocomposites [6] as well as the role of particles arrangement on mechanical properties. [13] The next challenge is to use polymers relevant in the industrial word poly(styrenecobutadiene), SBR, or natural rubber, NR, for instance which are more convenient for large strain tests than polyacrylates. The latter are in fact quite fragile mechanically. In the case of SBR and NR, however, it is rather difficult to polymerize the monomer in the presence of particles. The project will thus consist in mimicking the industrial mixing process grafting and/or adsorbing polymer chains and dispersing them afterwards in the polymer matrix In previous NMR work, we have developed quantitative approaches to the determination of the phase composition in dynamically heterogeneous materials, based on simple 1 Hlow field spectrometers. [14] Generally, the distinction is based upon the orientation dependence of interproton dipolar couplings and their potential averaging due to fast rotational motions of the molecules. Thus, immobile regions associated with strong dipolar couplings are characterized by quickly decaying time domain signals (broad lines in the frequency domain spectra), while more mobile components are only subject to weak or almost negligible RDC, leading to slower signal decay. Using a set of spinecho based magnetization filters, signals belonging to differently mobile components can be measured separately, allowing for a determination of fitting parameters for simple free induction decay (FID) data. With such an approach, we have performed an indepth study of the phases that can be identified in the PEAbased model systems described above. Parts of these results have been published recently, [15] and we here summarize these and some more current findings. Fig. 2a shows a typical FID from a highly filled PEA network, where three components can be identified: glassy (fully rigid), strongly immobilized (intermediate: only local, highly anisotropic smallamplitude mobility) and mobile (network chains and free chains. The total amount of interphase material (glassy + intermediate) is seen to reach up to 20% of the overall polymer signal. Detailed temperaturedependent studies (Fig. 2b) provided a direct proof the hypothesis on the softening of potential glassy bridges between fillers that, according to our model, [5] may explain the temperaturedependent decrease of (a) Lowfield 1 H NMR freeinduction decay data reflecting quantitatively interphases of reduced mobility in PEAbased nanocomposites. (b) Temperature dependence of the three distin guishable fit components, demonstrating an apparently increased glass transition temperature of the interphase material. (c) Relation of the amount of interphase material with the known inner surface (total surface area per volume) of different samples for two cases of different surface interaction. See ref. [15]. the reinforcement. A notable difference was found between the materials that are just characterized by silica particle surface that provide physical adsorption sites for the polymer, and those that have a high density of chemical surface grafting sites (Fig. 2c). We stress that even in the former systems, significant amounts of immobilized polymer could be evidenced. Currently, we are analyzing data from NMR spin diffusion experiments, [14] which are able to provide estimates of the thickness of the different domains and their spatial arrangement. First results are consistent with estimates based on the data in Fig. 2 that indicate a total interphase thickness of 5 6 nm at the lowest temperatures, as simply estimated from the determined volume fractions and the known internal surfaces. This corrects our previous lower, less quantitative results. [8] Analyzing indepth the spin diffusion across the three distinguishable phases, we A65

4 Articles have indications that the region of intermediate mobility does not simply form a homogenous layer around the glassy shell, but is inhomogeneously distributed. Finally, we used the 1 H MQ NMR method to probe the homogeneity of the mobile network phase in these systems. The results are summarized in terms of RDC (crosslink density) distributions in Fig. 3, and they differ significantly in some aspects from previous findings on commercially relevant systems, refs. [4,10] and Fig. 1c. First, the PEA networks appear much more inhomogeneous (note the log scale), which is attributed to the more complex spin system (side chain with lower RDC) and inhomogeneities intrinsic to the crosslinking process in this system. So even though the systems nicely exhibit average NMR detected crosslink densities that follow the trend expected for increasing crosslinker concentrations (Fig. 3a), the intrinsic width of the distributions poses limitations to a fully detailed analysis. This point will be improved upon by way of the up coming model composites based on NR, with their high intrinsic homogeneity. However, the findings for the filled PEA systems are also rather clear already: while the fillers with only physical bonds to the polymer phase (Fig. 3b) lead to no detectable changes of the rubber matrix, in analogy to our previous work (Fig. 1c), the fillers with dense grafts (Fig. 3c) significantly affect the matrix in that its crosslink density is generally increased and appears more inhomogeneous. The latter effect is seen in terms of broader peaks and shoulders on the highcrosslink side of the distribution functions, with even a trend to bimodality for the samples with the highest internal surface. These results give a convincing demonstration of the changes of the polymer matrix as arising from welldispersed highsurface nanofillers. Ongoing mechanical studies on these and the new model systems, and in particular on systems with controlled nanoparticle aggregation states, in combination with more refined computer simulations, will help in elucidating the relevance of polymer interphases with modified properties in general. A second, important aspect of the NMR part of the project is concerned with MQ NMR on deformed (stretched or compressed) samples, giving access to the orientation distribution and stretching states of the network chains. In this way, we seek to address the question whether in filled systems there is an inhomogeneous local strain distribution that may play a role in determining the unusual mechanical properties (high reinforcement, Payne and Mullins effects). In unfilled elastomers quite far above g, the effect of uniaxial strain on the distribution of residual NMR interactions (related to local strain at the scale of network chains) has been analyzed within the confines of standard rubber elasticity theories and the assumption of affine deformation. [16] In this case, the degree of anisotropy induced upon stretching is related directly to the average residual interaction measured in the relaxed state. In filled elastomers, a first evidence for a local strain distribution was obtained. [17] The distribution of local strain (at a given macroscopic strain) was shown to be related to the filler morphology and dispersion state. MQ NMR will give quantitative access to the distribution of local chain stretching (or equivalently local strain) at a given macroscopic strain, as regards both the magnitude and the orientation (local 3D effects). To discriminate magnitude and orientation effects on the distribution of residual couplings, the orientation of the stretching axis with respect to B 0 is varied. The angular variation gives access to orientation effect. Then, by combining experiments done at many different orientations, an effective powder spectrum can be reconstructed. Preliminary work has shown that the proposed analysis is indeed feasible. This analysis of the residual NMR interactions (MQ signal) can then be done as a function of the macroscopic strain imposed to the sample. We will then correlate the obtained distributions of residual NMR interactions in stretched samples to the tuned surface interactions and to the related heterogeneities of elastic modulus and the local (gradient of) mobility within the matrix. RDC distributions reflecting local crosslink density distributions as derived from 1 H lowfield MQ NMR experiments, based on data from ref. [15]. (a) PEA networks with varying amount of crosslinker given in wt%. (b,c) PEA networks with 0.3% crosslinker and varying amounts of welldispersed silica spheres that are modified so as to provide (b) just favourable adsorptive interactions or (c) a high density of chemical bonds (grafts) between the particles and the elastomer. As described above, elastomers filled with carbon black or silica particles have a shear modulus much (up to a few 100 times) higher than that of the pure elastomer and exhibit a high dissipative efficiency. Another important feature is their non linear behaviour. When submitted to deformations with ampli A66

5 tudes γ of the order of a few percent or more, the elastic modulus '(ω) decreases down to values much smaller than the value in the linear regime: this is the socalled Payne effect. During subsequent deformations, the elastic modulus in the linear regime is smaller than that of the initial system, but recovers progressively (at least partially) to the initial value: this is the so called Mullins effect. Recently, some of us have proposed a mesoscale model that explains these basic features. [18] The model is based on the presence of a glassy layer around the fillers when the interaction between the matrix and the fillers is sufficiently strong, [7,8,13] see Fig. 2 for our experimental quantification of this effect. We have proposed that the mechanical properties of nano filled elastomers are governed by the kinetics of rupture and re birth of glassy bridges which link neighbouring nanoparticles and from large rigid clusters of finite lifetimes. These lifetimes depend on various parameters such as temperature, nanoparticle matrix interactions, and distance between neighbouring fillers. Most importantly, these lifetimes depend on the deformation history of the samples. We have shown that the unusual non linear and plastic behaviour of these systems can be predicted by this death and rebirth process. A major challenge of the physics of filled elastomers is that the relevant space and time scales are very large compared to molecular scales. Thus, they are totally inaccessible to numerical simulations at the molecular scale, by many orders of magnitude. One must thus devise mesoscale models. Since numerical simulations cannot cover more than 67 decades in time, it is nevertheless an impossible task to address all the issues mentioned above in a single picture. Depending on the issues of interest, one must primarily focus on some particular aspect of the physical behaviour and use a coarsegrained description of the system. Two different scales are of particular interest. (i) A scale of about ten nanometers, corresponding to confined polymers layers, e.g. between two fillers, or two thin films deposited on a substrate, and (ii) the scale of a few hundreds of nanometers, corresponding to the size of filler aggregates. The latter bridges the gap between the former and the macroscopic continuous scale. ζ Schematics of a film at a temperature > g. In (a), the mechanical probe is at a distance z from the substrate larger than the size ξ of the slow aggregates. The slow aggregates can move freely around it, and the viscosity is smaller than the viscosity at g. In (b), the mechanical probe is closer to the substrate. Moving parallel to the film requires deforming slow aggregates: the viscosity is larger than that at the bulk g. An essential feature of polymers dynamics close to the glass transition is that it is strongly heterogeneous on a scale of a few nanometers, typically 3 nm. [19] Some of us have proposed that these dynamical heterogeneities correspond to density fluctu ations and that the macroscopic dynamics is controlled by the slowest percolating subunits. [20,21] This socalled "Percolation of Free Volume Distribution" (PFVD) model [22] allows to explain: (a) the heterogeneous nature of the dynamics, (b) the violation of the Stokes law observed for small probes, (c) essential features of ageing and rejuvenation, and (d) the shift of glass transition at interfaces. Fig. 4 illustrates the implications on the local mechanical properties of this films. The predicted glass transition temperature at a distance z from an interface is described by β 1/ν ( ) 1+, (1) where T g is the bulk glass transition temperature of the pure rubber. The exponent ν 0.88 is the critical exponent for the correlation length in 3D percolation. The value of the length β depends on the polymersubstrate interactions. For strong inter actions, it is of the order 1 nm. In its current development the model does not incorporate the description of the mechanical behaviour explicitly, for instance for calculating a storage and a dissipative modulus. It also does not include the effect of imposed deformation on the dynamical state (e.g. plastic deformation of polymers). One aim of this project will be to extend the PFVD model in order to describe and calculate the (linear and nonlinear) mechanical properties of confined polymers. We will thus be able to describe the evolution of a confined polymer layer under imposed deformations with a 23 nm scale resolution and on time scales spanning from 10 ns to 10 4 s typically. For this purpose, we will develop a 3D model, which we will solve by numerical simulations. In this 3D model, the basic units will be the subunits (3 nm) of dynamical heterogeneities. Their dynamical evolution (aging/rejuvenating) will be coupled to the stress field which results from the imposed deformations. We will thus describe the stress field at the nanometer scale (23 nm), as well as the strain field, and the dynamical state of each of the subunits. The PFVD model was used by Berriot et al. [5 8] for explaining the microscopic origin of the reinforcement in filled elastomers, as a consequence of the presence of a gradient of glass transition temperature around the fillers, as described by Eq. (1) and illustrated in Fig. 5. This provided the link between thin films dynamics (a few tens of nanometers) and the physical behaviour of filled elastomers. This equivalence between thin film dynamics and filled elastomer properties was subsequently stressed by experimental [23] and simulation [24] studies. In the presence of a local stress σ, we assume that the glass transition temperature in between two fillers is given by 1/ ν β σ σ (, ) 1+ (2) The first term in the right hand side of Eq. (2) represents the effect of the fillermatrix interactions. The second term is the decrease of g due to the local stress, which is the plasticizing A67

6 Articles effect of an applied stress. depends on the polymer. This parameter is known from macroscopic experiments. It relates the yield stress σ y to the temperature and the polymer glass transition temperature g by σ y = ( g ), and is typically of the order 10 6 Pa/K. The macroscopic stress in a filled elastomer is supported by the glassy polymer fraction which bridges two neighboring filler aggregates. Aggregates of about 100 nm made of primary particles of 10 nm are schematized. They are surrounded by a glassy layer which is sketched. The fraction of glassy polymer in a section normal to the applied stress is Σ ~ 1%. The macroscopic deformation is amplified between the fillers by a factor typically l ~ 10, which results in a macroscopic modulus G of the order 10 7 to 10 8 Pa. When glassy layers overlap, the macroscopic shear modulus ' is related to the shear modulus of the glassy polymer ' g through geometrical effects. Indeed, a macroscopic deformation ε is amplified locally in between the fillers by an amplification factor λ, which is the ratio between the diameter of the fillers and the distance between two neighboring fillers. In a plane normal to the direction of elongation, the stress is supported by glassy bridges which represent an area fraction Σ 1. Both parameters λ and Σ depend on the considered systems. The macroscopic modulus is thus given by λσ. (3) 100 nm Assuming that the fillers are spherical particles of 10 nm dia meter with typical interparticle distance of a few nanometers, we deduce that λ is of order a few units and Σ is of order a few 10 2, depending on the ratio between the glassy layer thickness and the nearest neighbor distance. Since ' g 10 9 Pa, we obtain a macroscopic shear modulus of about 10 8 Pa, which corresponds to very strong reinforcement. Consider a macroscopic deformation ε of a few percent. The local stress σ is then of order σ λε' g 10 8 Pa. With 10 6 Pa.K 1, a local g reduction of 100 K is obtained. Therefore, glassy bridges yield, which results in a lowering of the shear modulus, for macroscopic deformations of order a few percent. The glassy bridges are not permanent, rather, they break under applied strain. Within a glassy bridge in between two neighbouring particles, at equilibrium, we assume that the polymer has locally the dominant relaxation time τ α given by the WilliamLandelFerry (WLF) law of the corresponding polymer, modified by the g shift due to interfacial effects and the local stress σ. We assume that the breaking times of glassy bridges are comparable to the local dominant relaxation times τ α of the glassy bridges. The breaking time is thus given by ( (, σ )) 1( (, σ )) = τ + ( (, σ )) τ (, ) τ log α σ log (4) = τ 2 Here, τ g = 100 s (the relaxation time at g ) and is the temperature. C 1 and C 2 are the WLF parameters of the considered polymer. Eq. (4) gives the equilibrium value of the breaking time, which is obtained when the distance z, the local stress σ and the temperature have been maintained fixed for a long time. In general, the breaking time depends on the history of the glassy bridge and is denoted by τ α (). We assume that, at any time, a glassy bridge has a probability for breaking per unit time, d/d, given by d d = α (5) ( ) where α is a number of order 1, but smaller than 1. When a glassy bridge breaks, the local stress σ is relaxed and drops to a much smaller value, which is the rubbery contribution. Immediately after breaking, we assume that τ α relaxes to a value 1 τ min γ, where γ denotes the local deformation rate. In practice, typical deformation rates in our simulations are of order γ 0.1 s 1. The local breaking time τ α () undergoes a subsequent evolution, analogous to an ageing process. Thus the evolution of the breaking time of a glassy bridge, τ α (), is given by if τ α τ α ( ) = 1 (6) τ α ( (, )) ( ) τ σ. (7) By definition, we set the time τ α to be bounded by the time τ WLF ( g (z,σ)) given by Eq. (4). Eqs. (5), (6) and (7) describe the evolution of the local breaking times and lead to very complex behavior. When simulated in the presence of a few thousand beads, the evolution of these relaxation times deter mines the mechanical behavior of filled elastomers, enabling to explain or predict very specific nonlinear behaviours of filled elastomers. [7] The research project of the DINaFil consortium aims at an in depth understanding of the physical properties of filled elastomers. As highlighted in the artcile, it combines (i) the synthesis of wellcontrolled model systems, employing concepts from surface chemistry and colloid science, (ii) the application of advanced NMR techniques for the quantitative study of immobilized polymer phases and fillerinduced inhomogeneities in the rubber matrix, and (iii) the molecular characterization of local deformations in samples studied under strain. These studies are supplemented by dielectric and mechanical spectroscopy. A major goal consists in feeding the experimental insights into multiscale computer simulations in order to test and improve predictive theoretical models of filledelastomer behavior. A68

7 So far, we have been able to quantify exactly the temperature dependent content of polymer involved in glassy layers between the filler and the changes in the elastomer matrix in previously established model systems based upon poly(ethyl acrylate), and the studies are currently extended to other polymers. Our NMR techniques proved applicable to the study of strained samples, from which we are currently deducing the distribution of local strain. With the recent improvements in our theoretical model that is based on the temperature and yielding behavior of glassy bridges between the filler particles, we are confident that the project will contribute significantly to the development of rationaldesign approaches of filled elastomer materials. [1] J. E. Mark, B. Erman, F. R. Eirich,,Elsevier,Amsterdam. [2] M.J. Wang,,, A69

8 Articles [3] M. Klüppel,.,,186. [4] A. Mujtaba, M. Keller, S. Ilisch, H.J Radusch, T. ThurnAlbrecht, K. Saalwchter, M. Beiner, [5] H. Montes, F. Lequeux, J. Berriot,,, [6] J.Berriot,H.Monts,F.Lequeux,D.Long,P.Sotta,L.Monnerie,.,,50. [7] J.Berriot,H.Monts,F.Lequeux,D.Long,P.Sotta,,, [8] J.Berriot,F.Lequeux,H.Montes,L.Monnerie,D.Long,P.Sotta,,, [9] J. G. Meier, J. W. Mani, M. Klüppel,,, [10] J. L. Valentn, I. MoraBarrantes, J. CarreteroGonzlez, M. A. LpezManchado, P. Sotta, D. R. Long, K. Saalwchter,,, [11] K. Saalwchter,.,,135. [12] J. Berriot, H. Montes, F. Martin, M. Mauger, W. PyckhoutHintzen, G. Meier, H. Frielinghaus,,, [14] M. Mauri, Y. Thomann, H. Schneider, K. Saalwchter,,, [15] A. Papon, K. Saalwchter, K. Schler, L. Guy, F. Lequeux, H. Montes,,, [16] P. Sotta, [17] S. Dupres, D. Long, P.A. Albouy, P. Sotta,,, 42, [18] S. Merabia, P. Sotta, D. R. Long,,, [19] M. D. Ediger,.,,99. [20] D. Long, F. Lequeux,,, 371. [21] S. Merabia, P. Sotta, D. Long,,, 189. [22] K. Chen, E. J. Saltzman, K. S. Schweizer,,, [23] P. Rittigstein, R. D. Priestley, L. J. Broadbelt, J. M. Torkelson,,, [24] V.Pryamitsyn,V.Ganesan,,, [13] H. Montes, A. Papon, L. Guy, T. Chausse F. Lequeux,,, A70